Arcane Topics in Economics and Philosophy, Interspersed with Various Distractions

September 18, 2008

How to Make Money in Vegas

What's the trick to make money in Vegas? Just keep playing to you get ahead.

Let's suppose you can bet $1, and get $2 with 48% probably, $0 with 52% probability.

First, bet $1. If you win, you're ahead $1. Quit.

If you lose, you're down $1, so bet $2. If you win, you're ahead $1. Quit.

If you lose, you're down $3, so bet $4. If you win, you're ahead $1. Quit.

And so on.

Your odds are 48% of being ahead after the first turn, 71% after the second turn, 82% after the third turn. By the sixth turn or so they're over 90%!

Wall Street, unlike Vegas, tends to give you positive expected returns. Nonetheless, I think a fallacy similar to the one contained in the above advice has plagued Wall Street repeatedly in the past couple of decades. The word "leverage" is a warning sign.

Comments

I hit on this strategy when I was obsessed with odds in middle school. As long as your existing money stock is infinite, I thought, you can't lose. Later on, of course, I started to understand that if rounds of betting took appreciable time the opportunity costs would outweight winnings. But now that I know about high finance I can ask: what if your credit is infinitely good, so you can have that stock at a much lower cost? Then you win even more easily! Right?

I'm sure this is evident to everyone, but with finite money, the Las Vegas strategy still loses assuming one gambles for an indefinite amount of time. You can actually beat the house, statistically, in a game like 21 using sophisticated counting and odds playing techniques, but that's pretty much the only game.

This isn't the Gambler's fallacy. It's called the Martingale betting system (look it up on wikipedia). It would succeed if you had unlimited wealth, number of bets, and time. But obviously, no one has that. The problem is that there is always a chance you'll lose a huge amount of money while the amount of money you can ever gain is very small. It's the opposite of what most people want which is a small chance of winning a huge amount and a large chance of losing a small amount with each roll. Instead, you have a small chance of losing a huge amount and a large chance of gaining a small amount with each roll.